Intermittent Cooperation in Path Planning for Selfish Agents

Itay Shedlezki, Noa Agmon

Keywords: Self-Interested Agents, Two-Player Games, Graph Navigation, Non- cooperative games, Motion and path planning

Abstract:

Multi-robot systems often involve autonomous agents navigating shared environments toward individual goals.
In such environments, the spatial and temporal structure of the task may create opportunities for intermittent, localized cooperation, such as jointly opening a heavy gate, synchronizing to pass a traffic light as a convoy, or temporarily forming a vehicle platoon to reduce traversal time. Such cooperation is often opportunistic and fragile: robots remain self-interested, coordination is local and temporary, and deviation is always possible. We study this setting for two agents through the \emph{Intermittent Cooperation-Based Two-Agent Path Planning} (IC2PP) problem, a shortest-path game on graphs in which agents navigate toward individual targets while optionally cooperating at specific nodes to reduce their own travel times. Although such cooperation can strictly benefit both agents, it is strategically fragile: agents may deviate at any point along their paths. While a joint strategy in which each agent follows its naive shortest path without considering cooperation may not necessarily form a Pure Nash Equilibrium (PNE), we characterize the structure of PNE joint strategies in IC2PP, and show that stable cooperation must follow a highly constrained form. We further prove that at least one PNE exists in every instance of IC2PP, and present a polynomial-time algorithm for enumerating all relevant PNEs. When multiple equilibria arise, we study coordination mechanisms based on bargaining-theoretic selection concepts and empirically compare equilibrium outcomes in terms of individual travel times and social welfare.

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Submission Number: 4